US8515082B2 - Method of and a device for generating 3D sound - Google Patents

Method of and a device for generating 3D sound Download PDF

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US8515082B2
US8515082B2 US12/066,506 US6650606A US8515082B2 US 8515082 B2 US8515082 B2 US 8515082B2 US 6650606 A US6650606 A US 6650606A US 8515082 B2 US8515082 B2 US 8515082B2
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input signals
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Jeroen Dirk Breebaart
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Koninklijke Philips NV
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    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04S—STEREOPHONIC SYSTEMS 
    • H04S7/00—Indicating arrangements; Control arrangements, e.g. balance control
    • H04S7/30—Control circuits for electronic adaptation of the sound field
    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04S—STEREOPHONIC SYSTEMS 
    • H04S5/00—Pseudo-stereo systems, e.g. in which additional channel signals are derived from monophonic signals by means of phase shifting, time delay or reverberation 
    • G—PHYSICS
    • G10—MUSICAL INSTRUMENTS; ACOUSTICS
    • G10L—SPEECH ANALYSIS TECHNIQUES OR SPEECH SYNTHESIS; SPEECH RECOGNITION; SPEECH OR VOICE PROCESSING TECHNIQUES; SPEECH OR AUDIO CODING OR DECODING
    • G10L19/00—Speech or audio signals analysis-synthesis techniques for redundancy reduction, e.g. in vocoders; Coding or decoding of speech or audio signals, using source filter models or psychoacoustic analysis
    • G10L19/008—Multichannel audio signal coding or decoding using interchannel correlation to reduce redundancy, e.g. joint-stereo, intensity-coding or matrixing
    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04S—STEREOPHONIC SYSTEMS 
    • H04S3/00—Systems employing more than two channels, e.g. quadraphonic
    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04R—LOUDSPEAKERS, MICROPHONES, GRAMOPHONE PICK-UPS OR LIKE ACOUSTIC ELECTROMECHANICAL TRANSDUCERS; DEAF-AID SETS; PUBLIC ADDRESS SYSTEMS
    • H04R2499/00—Aspects covered by H04R or H04S not otherwise provided for in their subgroups
    • H04R2499/10—General applications
    • H04R2499/11—Transducers incorporated or for use in hand-held devices, e.g. mobile phones, PDA's, camera's
    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04S—STEREOPHONIC SYSTEMS 
    • H04S2400/00—Details of stereophonic systems covered by H04S but not provided for in its groups
    • H04S2400/01—Multi-channel, i.e. more than two input channels, sound reproduction with two speakers wherein the multi-channel information is substantially preserved
    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04S—STEREOPHONIC SYSTEMS 
    • H04S2420/00—Techniques used stereophonic systems covered by H04S but not provided for in its groups
    • H04S2420/01—Enhancing the perception of the sound image or of the spatial distribution using head related transfer functions [HRTF's] or equivalents thereof, e.g. interaural time difference [ITD] or interaural level difference [ILD]
    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04S—STEREOPHONIC SYSTEMS 
    • H04S2420/00—Techniques used stereophonic systems covered by H04S but not provided for in its groups
    • H04S2420/03—Application of parametric coding in stereophonic audio systems

Definitions

  • the invention relates to a device for processing audio data.
  • the invention also relates to a method of processing audio data.
  • the invention further relates to a program element.
  • the invention relates to a computer-readable medium.
  • audio sound especially 3D audio sound
  • 3D audio sound becomes more and more important in providing an artificial sense of reality, for instance, in various game software and multimedia applications in combination with images.
  • the sound field effect is thought of as an attempt to recreate the sound heard in a particular space.
  • 3D sound often termed as spatial sound, is sound processed to give a listener the impression of a (virtual) sound source at a certain position within a three-dimensional environment.
  • An acoustic signal coming from a certain direction to a listener interacts with parts of the listener's body before this signal reaches the eardrums in both ears of the listener.
  • the sound that reaches the eardrums is modified by reflections from the listener's shoulders, by interaction with the head, by the pinna response and by the resonances in the ear canal.
  • the body has a filtering effect on the incoming sound.
  • the specific filtering properties depend on the sound source position (relative to the head). Furthermore, because of the finite speed of sound in air, the significant inter-aural time delay can be noticed depending on the sound source position.
  • HRTFs Head-Related Transfer Functions
  • ATF anatomical transfer function
  • An HRTF database is constructed by measuring, with respect to the sound source, transfer functions from a large set of positions (typically at a fixed distance of 1 to 3 meters, and with a spacing of around 5 to 10 degrees in horizontal and vertical directions) to both ears. Such a database can be obtained for various acoustical conditions. For example, in an anechoic environment, the HRTFs capture only the direct transfer from a position to the eardrums, because no reflections are present. HRTFs can also be measured in echoic conditions. If reflections are captured as well, such an HRTF database is then room-specific.
  • HRTF databases are often used to position ‘virtual’ sound sources. By convolving a sound signal by a pair of HRTFs and presenting the resulting sound over headphones, the listener can perceive the sound as coming from the direction corresponding to the HRTF pair, as opposed to perceiving the sound source ‘in the head’, which occurs when the unprocessed sounds are presented over headphones.
  • HRTF databases are a popular means for positioning virtual sound sources. Applications in which HRTF databases are used include games, teleconferencing equipment and virtual reality systems.
  • a device for processing audio data a method of processing audio data, a program element and a computer-readable medium as defined in the independent claims are provided.
  • a device for processing audio data comprising a summation unit adapted to receive a number of audio input signals for generating a summation signal, a filter unit adapted to filter said summation signal dependent on filter coefficients resulting in at least two audio output signals, and a parameter conversion unit adapted to receive, on the one hand, position information, which is representative of spatial positions of sound sources of said audio input signals, and, on the other hand, spectral power information which is representative of a spectral power of said audio input signals, wherein the parameter conversion unit is adapted to generate said filter coefficients on the basis of the position information and the spectral power information, and wherein the parameter conversion unit is additionally adapted to receive transfer function parameters and generate said filter coefficients in dependence on said transfer function parameters.
  • a method of processing audio data comprising the steps of receiving a number of audio input signals for generating a summation signal and filtering said summation signal dependent on filter coefficients resulting in at least two audio output signals, receiving, on the one hand, position information, which is representative of spatial positions of sound sources of said audio input signals, and, on the other hand, spectral power information which is representative of a spectral power of said audio input signals, generating said filter coefficients on the basis of the position information and the spectral power information, and receiving transfer function parameters and generating said filter coefficients in dependence on said transfer function parameters.
  • a computer-readable medium in which a computer program for processing audio data is stored, which computer program, when being executed by a processor, is adapted to control or carry out the above-mentioned method steps.
  • a program element for processing audio data is provided in accordance with yet another embodiment of the invention, which program element, when being executed by a processor, is adapted to control or carry out the above-mentioned method steps.
  • Processing audio data according to the invention can be realized by a computer program, i.e. by software, or by using one or more special electronic optimization circuits, i.e. in hardware, or in a hybrid form, i.e. by means of software components and hardware components.
  • the characterizing features according to the invention particularly have the advantage that virtualization of multiple virtual sound sources is enabled with a computational complexity that is almost independent of the number of virtual sound sources.
  • multiple simultaneous sound sources may be advantageously synthesized with a processing complexity that is roughly equal to that of a single sound source.
  • real-time processing is advantageously possible, even for a large number of sound sources.
  • a further object envisaged by the embodiments of the invention is to reproduce a sound pressure level at a listener's eardrums that is equivalent to the sound pressure that would be present if an actual sound source were placed in the location (3D position) of the virtual sound source.
  • the applications according to the invention are capable of rendering virtual acoustic sound sources giving a listener the impression that the sources are at their correct spatial location.
  • Embodiments of the device for processing audio data will now be described. These embodiments may also be applied for the method of processing audio data, for the computer-readable medium and for the program element.
  • the relative level of each individual audio input signal can be adjusted to some extent on the basis of spectral power information. Such adjustments can only be done within limits (for example, a maximum change of 6 or 10 dB). Usually, the effect of distance is much greater than 10 dB, due to the fact that the signal level scales approximately linearly with the inverse of the sound source distance.
  • the device may additionally comprise a scaling unit adapted to scale the audio input signals based on gain factors.
  • the parameter conversion unit may additionally be adapted advantageously to receive distance information representative of distances of sound sources of the audio input signals and to generate the gain factors based on said distance information.
  • the gain factor may decrease by one over the distance.
  • the power of the sound sources may thereby be modeled or adapted in accordance with acoustical principles.
  • the gain factors may reflect air absorption effects.
  • a more realistic sound sensation may be achieved.
  • the filter unit is based on Fast Fourier-Transform (Ft). This may allow efficient and quick processing.
  • HRTF databases may comprise a limited set of virtual sound source positions (typically at a fixed distance and 5 to 10 degrees of spatial resolution). In many situations, sound sources have to be generated for positions in between measurement positions (especially if a virtual sound source is moving across time). Such a generation requires interpolation of available impulse responses. If HRTF databases comprise responses for vertical and horizontal directions, an interpolation has to be performed for each output signal. Hence, a combination of 4 impulse responses for each headphone output signal is required for each sound source. The number of required impulse responses becomes even more important if more sound sources have to be “virtualized” simultaneously.
  • HRTF model parameters and parameters representing HRTFs may be interpolated in between the spatial resolutions that are stored.
  • a main field of application of the system according to the invention is processing audio data.
  • the system can be embedded in a scenario in which, in addition to the audio data, additional data are processed, for instance, related to visual content.
  • the invention can be realized in the flame of a video data-processing system.
  • the device according to the invention may be realized as one of the devices of the group consisting of a vehicle audio system, a portable audio player, a portable video player, a head-mounted display, a mobile phone, a DVD player, a CD player, a hard disk-based media player, an internet radio device, a public entertainment device and an MP3 player.
  • a vehicle audio system a portable audio player, a portable video player, a head-mounted display, a mobile phone, a DVD player, a CD player, a hard disk-based media player, an internet radio device, a public entertainment device and an MP3 player.
  • any other application is possible, for example, in telephone-conferencing and telepresence; audio displays for the visually impaired; distance learning systems and professional sound and picture editing for television and film as well as jet fighters (3D audio may help pilots) and pc-based audio players.
  • FIG. 1 shows a device for processing audio data in accordance with a preferred embodiment of the invention.
  • FIG. 2 shows a device for processing audio data in accordance with a further embodiment of the invention.
  • FIG. 3 shows a device for processing audio data in accordance with an embodiment of the invention, comprising a storage unit.
  • FIG. 4 shows in detail a filter unit implemented in the device for processing audio data shown in FIG. 1 or FIG. 2 .
  • FIG. 5 shows a further filter unit in accordance with an embodiment of the invention.
  • a device 100 for processing input audio data X i in accordance with an embodiment of the invention will now be described with reference to FIG. 1 .
  • the device 100 comprises a summation unit 102 adapted to receive a number of audio input signals X i for generating a summation signal SUM from the audio input signals X i .
  • the summation signal SUM is supplied to a filter unit 103 adapted to filter said summation signal SUM on the basis of filter coefficients, i.e. in the present case a first filter coefficient SF 1 and a second filter coefficient SF 2 , resulting in a first audio output signal OS 1 and a second audio output signal OS 2 .
  • filter coefficients i.e. in the present case a first filter coefficient SF 1 and a second filter coefficient SF 2
  • device 100 comprises a parameter conversion unit 104 adapted to receive, on the one hand, position information V i , which is representative of spatial positions of sound sources of said audio input signals X i , and, on the other hand, spectral power information S i , which is representative of a spectral power of said audio input signals X i , wherein the parameter conversion unit 104 is adapted to generate said filter coefficients SF 1 , SF 2 on the basis of the position information V i and the spectral power information S i corresponding to input signal, and wherein the parameter conversion unit 104 is additionally adapted to receive transfer function parameters and generate said filter coefficients additionally in dependence on said transfer function parameters.
  • position information V i which is representative of spatial positions of sound sources of said audio input signals X i
  • S i which is representative of a spectral power of said audio input signals X i
  • the parameter conversion unit 104 is adapted to generate said filter coefficients SF 1 , SF 2 on the basis of the position information V i and
  • FIG. 2 shows an arrangement 200 in a further embodiment of the invention.
  • the arrangement 200 comprises a device 100 in accordance with the embodiment shown in FIG. 1 and additionally comprises a scaling unit 201 adapted to scale the audio input signals X i based on gain factors g i .
  • the parameter conversion unit 104 is additionally adapted to receive distance information representative of distances of sound sources of the audio input signals and generate the gain factors g i based on said distance information and provide these gain factors g i to the scaling unit 201 .
  • an effect of distance is reliably achieved by means of simple measures.
  • a system 300 which comprises an arrangement 200 in accordance with the embodiment shown in FIG. 2 and additionally comprises a storage unit 301 , an audio data interface 302 , a position data interface 303 , a spectral power data interface 304 and a HRTF parameter interface 305 .
  • the storage unit 301 is adapted to store audio waveform data and the audio data interface 302 is adapted to provide the number of audio input signals X i based on the stored audio waveform data.
  • the audio waveform data is stored in the form of pulse code-modulated (PCM) wave tables for each sound source.
  • PCM pulse code-modulated
  • waveform data may be stored additionally or separately in another form, for instance, in a compressed format as in accordance with the standards MPEG-1 layer3 (MP3), Advanced Audio Coding (AAC), AAC-Plus, etc.
  • MP3 MPEG-1 layer3
  • AAC Advanced Audio Coding
  • AAC-Plus etc.
  • position information V i is stored for each sound source and the position data interface 303 is adapted to provide the stored position information V i .
  • the preferred embodiment is directed to a computer game application.
  • the position information V i varies over time and depends on the programmed absolute position in a space (i.e. virtual spatial position in a scene of the computer game), but it also depends on user action, for example, when a virtual person or user in the game scene rotates or changes his/her virtual position, the sound source position relative to the user changes or should change as well.
  • the number of simultaneous sound sources may be, for instance, as high as sixty-four (64) and, accordingly, the audio input signals X i will range from X 1 to X 64 .
  • the interface unit 302 provides the number of audio input signals X i based on the stored audio waveform data in frames of size n.
  • each audio input signal X i is provided with a sampling rate of eleven (11) kHz.
  • Other sampling rates are also possible, for example, forty-four (44) kHz for each audio input signal X i .
  • the input signals X i of size n i.e. X i [n] are combined into a summation signal SUM, i.e. a mono signal m[n], using gain factors or weights g i per channel according to equation one (1):
  • the gain factors g i are provided by the parameter conversion unit 104 based on stored distance information accompanied by the position information V i as explained above.
  • the position information V i and spectral power information S i parameters typically have much lower update rates, for example, an update every eleventh (11) millisecond.
  • the position information V i per sound source consists of a triplet of azimuth, elevation and distance information.
  • Cartesian coordinates (x,y,z) or alternative coordinates may be used.
  • the position information may comprise information in a combination or a subset, i.e. in terms of elevation information and/or azimuth information and/or distance information.
  • the gain factors g i [n] are time-dependent. However, given the fact that the required update rate of these gain factors is significantly lower than the audio sampling rate of the input audio signals X i , it is assumed that the gain factors g i [n] are constant for a short period of time (as mentioned before, around eleven (11) milliseconds to twenty-three (23) milliseconds). This property allows frame-based processing, in which the gain factors g i are constant and the summation signal m[n] is represented by equation two (2):
  • Filter unit 103 will now be explained with reference to FIGS. 4 and 5 .
  • the filter unit 103 shown in FIG. 4 comprises a segmentation unit 401 , a Fast Fourier Transform (FFT) unit 402 , a first sub-band grouping unit 403 , a first mixer 404 , a first combination unit 405 , a first inverse-FFT unit 406 , a first overlap-adding unit 407 , a second sub-band grouping unit 408 , a second mixer 409 , a second combination unit 410 , a second inverse-FFT unit 411 and a second overlap-adding unit 412 .
  • the first sub-band grouping unit 403 , the first mixer 404 and the first combination unit 405 constitute a first mixing unit 413 .
  • the second sub-band grouping unit 408 , the second mixer 409 and the second combination unit 410 constitute a second mixing unit 414 .
  • the segmentation unit 401 is adapted to segment an incoming signal, i.e. the summation signal SUM and signal m[n], respectively, in the present case, into overlapping frames and to window each frame.
  • a Hanning window is used for windowing.
  • Other methods may be used, for example, a Welch, or triangular window.
  • FFT unit 402 is adapted to transform each windowed signal to the frequency domain using an FFT.
  • the actual processing consists of modification (scaling) of each FFT bin in accordance with a respective scale factor that was stored for the frequency range to which the current FFT bin corresponds, as well as modification of the phase in accordance with the stored time or phase difference.
  • the difference can be applied in an arbitrary way (for example, to both channels (divided by two) or only to one channel).
  • the respective scale factor of each FFF bin is provided by means of a filter coefficient vector, i.e. in the present case the first filter coefficient SF 1 provided to the first mixer 404 and the second filter coefficient SF 2 provided to the second mixer 409 .
  • the filter coefficient vector provides complex-valued scale factors for frequency sub-bands for each output signal.
  • the modified left output frames L[k] are transformed to the time domain by the inverse FFT unit 406 obtaining a left time-domain signal, and the right output frames R[k] are transformed by the inverse FFT unit 411 obtaining a right time-domain signal.
  • an overlap-add operation on the obtained time-domain signals results in the final time domain for each output channel, i.e. by means of the first overlap-adding unit 407 obtaining the first output channel signal OS 1 and by means of the second overlap-adding unit 412 obtaining the second output channel signal OS 2 .
  • the filter unit 103 ′ shown in FIG. 5 deviates from the filter unit 103 shown in FIG. 4 in that a decorrelation unit 501 is provided, which is adapted to supply a decorrelation signal to each output channel, which decorrelation signal is derived from the frequency-domain signal obtained from the FFT unit 402 .
  • a first mixing unit 413 ′ similar to the first mixing unit 413 shown in FIG. 4 is provided, but it is additionally adapted to process the decorrelation signal.
  • a second mixing unit 414 ′ similar to the second mixing unit 414 shown in FIG. 4 is provided, which second mixing unit 414 ′ of FIG. 5 is also additionally adapted to process the decorrelation signal.
  • the two output signals L[k] and R[k] (in the FFT domain) are then generated as follows on a band-by-band basis:
  • D[k] denotes the decorrelation signal that is obtained from the frequency-domain representation M[k] according to the following properties:
  • the decorrelation unit 501 consists of a simple delay with a delay time of the order of 10 to 20 ms (typically one frame) that is achieved, using a FIFO buffer.
  • the decorrelation unit may be based on a randomized magnitude or phase response, or may consist of IIR or all-pass-like structures in the FFT, sub-band or time domain. Examples of such decorrelation methods are given in Engdeg ⁇ rd, Heiko Purnhagen, Jonas Rödén, Lars Liljeryd (2004): “Synthetic ambience in parametric stereo coding”, proc. 116th AES convention, Berlin, the disclosure of which is herewith incorporated by reference.
  • the decorrelation filter aims at creating a “diffuse” perception at certain frequency bands. If the output signals arriving at the two ears of a human listener are identical, except for a time or level difference, the human listener will perceive the sound as coming from a certain direction (which depends on the time and level difference). In this case, the direction is very clear, i.e. the signal is spatially “compact”.
  • each ear will receive a different mixture of sound sources. Therefore, the differences between the ears cannot be modeled as a simple (frequency-dependent) time and/or level difference. Since, in the present case, the different sound sources are already mixed into a single sound source, recreation of different mixtures is not possible. However, such a recreation is basically not required because the human hearing system is known to have difficulty in separating individual sound sources based on spatial properties.
  • the dominant perceptual aspect in this case is how different the waveforms at both ears are if the waveforms for time and level differences are compensated. It has been shown that the mathematical concept of the inter-channel coherence (or maximum of the normalized cross-correlation function) is a measure that closely matches the perception of spatial ‘compactness’.
  • the main aspect is that the correct inter-channel coherence has to be recreated in order to evoke a similar perception of the virtual sound sources, even if the mixtures at both ears are wrong.
  • This perception can be described as “spatial diffuseness”, or lack of “compactness”. This is what the decorrelation filter, in combination with the mixing unit, recreates.
  • the parameter conversion unit 104 determines how different the waveforms would have been in the case of a regular HRTF system if these waveforms had been based on single sound source processing. Then, by mixing the direct and decorrelated signal differently in the two output signals, it is possible to recreate this difference in the signals that cannot be attributed to simple scaling and time delays.
  • a realistic sound stage is obtained by recreating such a diffuseness parameter.
  • the parameter conversion unit 104 is adapted to generate filter coefficients SF 1 , SF 2 from the position vectors V i and the spectral power information S i for each audio input signal X i .
  • the filter coefficients are represented by complex-valued mixing factors h xx,b .
  • Such complex-valued mixing factors are advantageous, especially in a low-frequency area. It may be mentioned that real-valued mixing factors may be used, especially when processing high frequencies.
  • the values of the complex-valued mixing factors h xx,b depend in the present case on, inter alia, transfer function parameters representing Head-Related Transfer Function (HRTF) model parameters P 1,b ( ⁇ , ⁇ ), P r,b ( ⁇ , ⁇ ) and ⁇ b ( ⁇ , ⁇ ):
  • HRTF Head-Related Transfer Function
  • the HRTF model parameter P 1,b ( ⁇ , ⁇ ) represents the root-mean-square (rms) power in each sub-band b for the left ear
  • the HRTF model parameter P r,b ( ⁇ , ⁇ ) represents the rms power in each sub-band b for the right ear
  • the HRTF model parameter ⁇ b ( ⁇ , ⁇ ) represents the average complex-valued phase angle between the left-ear and right-ear HRTF.
  • HRTF model parameters are provided as a function of azimuth ( ⁇ ) and elevation ( ⁇ ). Hence, only HRTF parameters P 1,b ( ⁇ , ⁇ ), P r,b ( ⁇ , ⁇ ) and ⁇ b ( ⁇ , ⁇ ) are required in this application, without the necessity of actual HRTFs (that are stored as finite impulse-response tables, indexed by a large number of different azimuth and elevation values).
  • the HRTF model parameters are stored for a limited set of virtual sound source positions, in the present case for a spatial resolution of twenty (20) degrees in both the horizontal and vertical direction. Other resolutions may be possible or suitable, for example, spatial resolutions of ten (10) or thirty (30) degrees.
  • an interpolation unit may be provided, which is adapted to interpolate HRTF model parameters in between the spatial resolution, which are stored.
  • a bi-linear interpolation is preferably applied, but other (non-linear) interpolation schemes may be suitable.
  • the transfer function parameters provided to the parameter conversion unit may be based on, and represent, a spherical head model.
  • the spectral power information S i represents a power value in the linear domain per frequency sub-band corresponding to the current frame of input signal X i .
  • S i [( ⁇ 2 0,i , ⁇ 2 1,i , . . . , ⁇ 2 b,i ]
  • the number of frequency sub-bands (b) in the present case is ten (10). It should be mentioned here that spectral power information S i may be represented by power value in the power or logarithmic domain, and the number of frequency sub-bands may achieve a value of thirty (30) or forty (40) frequency sub-bands.
  • the power information S i basically describes how much energy a certain sound source has in a certain frequency band and sub-band, respectively. If a certain sound source is dominant (in terms of energy) in a certain frequency band over all other sound sources, the spatial parameters of this dominant sound source get more weight on the ‘composite’ spatial parameters that are applied by the filter operations. In other words, the spatial parameters of each sound source are weighted by using the energy of each sound source in a frequency band to compute an averaged set of spatial parameters.
  • An important extension to these parameters is that not only a phase difference and level per channel is generated, but also a coherence value. This value describes how similar the waveforms should be that are generated by the two filter operations.
  • the input signals X i are assumed to be mutually independent in each frequency band b:
  • the power of the output signal L[k] in each sub-band b should be equal to the power in the same sub-band of a signal L′[k]:
  • the power of the output signal R[k] in each sub-band b should be equal to the power in the same sub-band of a signal R′[k]:
  • the average complex angle between signals L[k] and M[k] should equal the average complex phase angle between signals L′[k] and M[k] for each frequency band b:
  • the average complex angle between signals R[k] and M[k] should equal the average complex phase angle between signals R′[k] and M[k] for each frequency band b:
  • ⁇ b,i denotes the energy or power in sub-band b of signal X i
  • ⁇ i represents the distance of sound source i.
  • the filter unit 103 is alternatively based on a real-valued or complex-valued filter bank, i.e. IIR filters or FIR filters that mimic the frequency dependency of h xy,b , so that an FFT approach is not required anymore.
  • the audio output is conveyed to the listener either through loudspeakers or through headphones worn by the listener.
  • Both headphones and loudspeakers have their advantages as well as shortcomings, and one or the other may produce more favorable results depending on the application.
  • more output channels may be provided, for example, for headphones using more than one speaker per ear, or a loudspeaker playback configuration.

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